Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
530 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 530 conjugacy classes of subgroups — too many to draw. Only its 103 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #20283782 | C2 | semidirect |
| 3. #20273133 | C2 | semidirect |
| 4. #20272553 | C2 | semidirect |
| 5. C53×#1525 | C2 | semidirect |
| 144. #1525 | D53 | semidirect |
| 169. C53 | #9069 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285141 | 2 |
| #20283782 | 2 |
| #20273133 | 2 |
| #20272553 | 2 |
| C53×#1525 | 2 |
| #9069 | 53 |